Effect of Fuel Doping in ICF Targets

ABSTRACT

Inertial Confinement Fusion (ICF) reactor chambers can be designed to contain an ICF target being imploded and capture the resulting energy output from the reaction. The exact amount of energy required to facilitate this implosion depends on the specific target design in use. An ICF target design and implosion mechanism which is more robust against non-uniformities, simpler to analyze and simpler to utilize would be advantageous in achieving practical energy generation. Ideally, the ICF target will be configured to achieve a uniform temperature and density profile when imploding with a variety of parameters not limited to the following: a central region having an areal density (ρr) less than 1 g/cm2 at ignition and approximately 1% of the entire mass to be a material having a Z between 6 and 47 inclusive. Once the parameters of the ICF target are selected, one can easily smooth both the temperature and density profiles in the fusion fuel of non-equilibrium ignition targets without preventing runaway burn or affecting margin parameters such as fall-line greatly.

CROSS-REFERENCE TO RELATED APPLICATIONS

This is a continuation-in-part of U.S. application Ser. No. 16/796,084, claiming priority to U.S. Provisional application Ser. No. 16/796,084 filed on Feb. 20, 2020, which is incorporated herein by reference.

BACKGROUND

Nuclear fusion by inertial confinement (Inertial Confinement Fusion, or “ICF”) utilizes nuclear fusion reactions to produce energy. In most types of ICF system, an external drive mechanism such as a laser delivers energy to a target containing nuclear fusion fuel. The target is designed to use this energy to compress, heat and ignite the fusion fuel within it. If a sufficient amount of fuel is compressed sufficiently and heated sufficiently, a self-sustaining fusion reaction can occur, in which energy produced by fusion reactions continues to heat the fuel (“ignition”). The inertia of the compressed fuel can keep it from expanding long enough for significant energy to be produced, before expansion of the fuel and the resultant cooling terminates the fusion reaction. Most conventional ICF target designs involve a spherical target which is imploded symmetrically from all directions, relying on stagnation of inwardly-accelerated fuel at the center of the sphere to produce the required densities and temperatures.

Production of the very high temperatures and densities required for fusion ignition may require a substantial amount of energy. The exact amount of energy required depends on the specific target design in use. In order to be useful for energy generation, the target must be capable of producing more energy from fusion reactions than was required to ignite it. In addition, the amount of energy required by the target must be physically and/or economically realizable by the drive mechanism being used.

For this reason, conventional ICF target designs have focused on achieving the required temperatures and densities as efficiently as possible. These designs are often complex in their construction and operation, and sensitive to imperfection in the target's manufacturing and to non-uniformity in the delivery of energy to the target from the drive mechanism. Imperfection and non-uniformity can lead to asymmetry in the target's implosion, which may reduce the densities and temperatures achieved, potentially below the threshold required for ignition. Furthermore, successful operation of these complex designs often requires achieving a precise balance between multiple competing physical processes, many of which are poorly understood and difficult to model. When actually constructed and deployed, these complex ICF target designs often fail to perform as their designers intended, and to date none have actually succeeded in producing ignition.

The NIF target exemplifies the conventional approach. The NIF target, as described in Haan, Physics of Plasmas 18, 051001 (2011), involves an outer ablator shell comprising primarily plastic or beryllium with various dopants, surrounding a shell of cryogenic DT ice, with a central void filled with low-density DT gas. The target is placed in a cylindrical hohlraum. The entire target assembly (hohlraum and target) is then placed in the target chamber where a laser consisting of 192 separate beamlines, with a total energy delivered to the hohlraum of up to 1.8 MJ, illuminates a plurality of spots on the inner surface of the hohlraum, producing a radiation field which fills the hohlraum. The radiation field ablates the ablator layer, and the reactive force of the ablator ablating implodes the target. The laser pulse is 18 nanoseconds long and is temporally tailored in order to drive a series of precisely-adjusted shocks into the target. The timing and energy level of these shocks are adjusted in order to achieve a quasi-isentropic, efficient implosion and compression of the shell of DT fuel. Stagnation of these shocks and inward-moving material at the center of the target is intended to result in the formation of a small “hotspot” of fuel, at a temperature of roughly 10 keV and a ρr of approximately 0.3 grams/cm², surrounded by a much larger mass of relatively cold DT fuel, and it is intended that the fuel in the “hotspot” will ignite, with fusion burn then propagating into the cold outer shell.

In practice, the NIF target has so far failed to ignite, achieving peak temperatures and densities of about 3 keV and a ρr of approximately 0.1 grams/cm² in the hotspot, short of the 10 keV and 0.3 grams/cm² anticipated to be required for ignition. There is no clear consensus on what has caused the failure of the NIF target to achieve ignition, but it appears that this failure may be partially due to low-order asymmetry in the hotspot formation and lower than expected implosion velocities.

An ICF target design and implosion mechanism which is more robust against non-uniformities, simpler to analyze and simpler to utilize would be advantageous in achieving practical energy generation through ICF.

SUMMARY

In Inertial Confinement Fusion target design, a deuterium and tritium (DT) fuel section having an areal density (ρr) less than 1 g/cm² at ignition, the fuel section tends to have a very non-uniform temperature profile which leads to non-equilibrium ignition and a non-uniform density profile. However, there is an optimal material and content for the fuel region for any given ICF target design. Once these parameters are selected, one can then smooth both the temperature and density profiles in the fuel of non-equilibrium ignition targets without preventing runaway burn or affecting margin parameters such as fall-line greatly.

DRAWINGS

FIG. 1 shows a single shell configuration of an ICF target.

FIG. 2 shows a double shell configuration of an ICF target.

FIG. 3 plots the temperature profile of the fuel region.

FIG. 4 plots the fall line parameter.

FIG. 5 plots the temperature profile of the varying degrees of Iron mixed into the fuel region.

FIG. 6 plots the Iron content in the fuel region versus the yield.

SPECIFICATION

Inertial Confinement Fusion reactor chambers can be designed to contain an ICF target being imploded and capture the resulting energy output from the reaction in the forms of neutrons, radiation, and/or debris. Such chambers can generally include a combination of neutron moderating layers, neutron absorbing layers, neutron shielding layers, radiation capturing layers, sacrificial layers, shock absorbers, tritium breeding layers, tritium breeders, coolant systems, injection nozzles, inert gas injection nozzles, sputterers, sacrificial coating injection nozzles, beam channels, target supporting mechanism, and/or purge ports, among others. ICF chambers can be any one of a variety of shapes: cylindrical, spherical, prolated spheroid, etc.

Specific material choice for the structures/elements of an ICF target is important, where indicated, as different isotopes of the same element undergo completely different nuclear refractions, and different elements may have different radiation opacities for specific frequencies. The differing solid densities of materials with similar atomic number (Z) is also important for certain design criteria.

The term “Z” refers to the atomic number of an element, the number of protons in the nucleus. At the pressures and temperatures involved in imploding and burning ICF targets, specific material properties that one observes in everyday life (hardness, strength, room temperature thermal conductivity, etc.) may be irrelevant, and the hydrodynamic behavior of a material can depend most strongly on the material's average atomic number, atomic mass number, and solid density.

As such, in discussing material requirements in ICF targets, it is convenient to discuss classes of material. For the purposes of the following discussion, the term “low-Z” will refer to materials with an atomic number of 1 through 5, inclusive of the endpoints (e.g., Hydrogen, Helium, Lithium, Beryllium, and Boron); the term “medium-Z” will refer to materials with an atomic number of 6 through 47, inclusive of the endpoints (i.e., any of the materials on a periodic table from Carbon to Silver according to its' atomic number); and the term “high-Z” will refer to materials with an atomic number of 48 and greater (i.e., Cadmium and above). By any known definition, an endpoint is the beginning or ending point of a range or interval and inclusive means that the endpoint is included. Unless otherwise stated, the use of these terms to describe a class of material for a specific function is intended only to suggest that this class of material may be particularly advantageous for that function, and not (for instance) that a “high-Z” material could not be substituted where a “medium-Z” material is suggested, or vice-versa.

The term “neutron” refers to a subatomic particle with no electrical charge. Their lack of a charge means that free neutrons generally have a greater free range in matter than other particles.

The term “proton” refers to a subatomic particle with a positive electrical charge.

The term “electron” refers to a subatomic particle with a negative electrical charge, exactly opposite to that of a proton and having less mass than a proton and a neutron.

The term “atom” refers to a particle of matter, composed of a nucleus of tightly bound protons and neutrons, with an electron shell. Each element has a specific number of protons. Atoms under ordinary conditions have the same number of electrons as protons, so that their charges cancel.

The term “isotope” refers to atoms of the same element that have the same number of protons, but a different number of neutrons. Isotopes of an element are generally identical chemically but have different probabilities of undergoing nuclear reactions. The term “ion” refers to a charged particle, such as a proton or a free nucleus.

The term “plasma” refers to the so-called fourth state of matter, beyond solid, liquid, and gas. Matter is typically in a plasma state when the material has been heated enough to separate electrons from their atomic nuclei.

The term “Bremsstrahlung radiation” refers to radiation produced by interactions between electrons and ions in a plasma. One of the many processes that can cool a plasma is energy loss due to Bremsstrahlung radiation.

The term “runaway burn” refers to a fusion reaction that heats itself and reaches a very high temperature. Because the D-T reaction rate increases with temperature, peaking at 67 keV, a D-T plasma heated to ignition temperatures may rapidly self-heat and reach extremely high temperatures, approximately 100 keV, or higher.

The term “approximately” and “about” refers a given value ranging plus/minus 15%. For example, the phrase “approximately 10 units” is intended to encompass a range of 8.5 units to 11.5 units.

FIG. 1 shows a single shell configuration (not to scale) of an ICF target. Target assembly 100 comprises a hohlraum 110 surrounding an ICF target 120. ICF target 120 comprises a high-Z shell 104 and a fuel region 102. Fuel region 102 may be filled with an equimolar mixture of deuterium and tritium (DT), wherein the deuterium and tritium are mixed throughout the fuel region. Deuterium and Tritium are a common and well-known fusion fuel mixture used in an ICF target. In some embodiments, fuel region 102 may have a higher ratio of deuterium to tritium, or conversely a higher ratio of tritium to deuterium. Fuel region 102 can be filled with a variety of different fusion fuel materials not limited to the following: pure deuterium, lithium deuteride, lithium tritide, or combination of a plurality of fusion fuel materials. Surrounding high-Z shell 104 is a drive region/ablator region (not shown). The high-Z shell 104 may implode, if sufficiently driven by ways known in the art, such as ablation of an outer ablator region or other methods known in the art. This inward motion of the high-Z shell 104 launches a shock into the fuel region 102 to sufficiently heat the fusion fuel mixture within fuel region 102; and simultaneously, the shell 104 compresses the fuel region 102 and causes it to ignite and burn a signification fraction of the fuel. When the laser reaches the ICF target, a shock is launched into the fuel region and the state of the fusion fuel material in the fuel region 102 transforms into a plasma. This phase transformation allows the mixture containing a plurality of different fusion fuel materials to blend/mix together within fuel region 102.

FIG. 2 depicts a double shell configuration (not to scale). Target assembly 200 is similar to target assembly 100. Target assembly 200 comprises a hohlraum 210 surrounding an ICF target 220 with a central spherical fuel region, the inner fuel region 202. Surrounding the inner fuel region 202 is an inner shell 204 and outer shell 208. In the space between the inner shell 204 and outer shell 208 is an outer fuel region 206. Inner fuel region 202 may be filled with an equimolar mixture of deuterium and tritium (DT), wherein the deuterium and tritium are mixed throughout the fuel region. In some embodiments, inner fuel region 202 may have a higher ratio of deuterium to tritium, or conversely a higher ratio of tritium to deuterium. Inner fuel region 202 can also be filled with a variety of different fusion fuel materials not limited to the following: pure deuterium, lithium deuteride, lithium tritide, or combination of a plurality of fusion fuel materials. Other materials, not limited to the following: pure deuterium, lithium deuteride, lithium tritide, or combination of a plurality of fusion fuel materials, may be substituted for the DT fuel in outer fuel region 206. Some of these materials may be inert, but we will nonetheless still refer to this region as the “outer fuel region” 206. Surrounding outer shell 208 is a drive region/ablator region (not shown). The outer shell 208 may implode, if sufficiently driven by ways known in the art, such as ablation of an outer ablator region (not shown) or other methods known in the art. This inward motion of the outer shell 208 launches a shock into the outer fuel region 206 which will launch a shock into the inner shell 204 and subsequently the inner fuel region 204. This in turn will sufficiently heat the outer fuel region 206 and inner fuel region 204, and simultaneously, the outer shell 208 will compress the outer fuel region 206, and subsequently the inner shell 204 will compress the inner fuel region 202 and cause it to ignite and burn a signification fraction of the fuel. When a laser reaches the ICF target, a shock launches into the fuel region and the state of the fusion fuel material in the fuel region 202 transforms into a plasma. This phase transformation allows the mixture of a plurality of different fusion fuel materials to blend/mix together within fuel region 202.

For simplicity we will refer to FIG. 1 , however this is also applicable to FIG. 2 . When the high-Z shell 104 implodes, this inward motion of the shell 104 will launch a shock into the fuel region 102, this shock will sufficiently heat the fusion fuel in fuel region 102, transforming the state of the fusion fuel material into a plasma, thus allowing the plurality of materials to mix throughout the fuel region. Simultaneously, the shell 104 compresses the fusion fuel in fuel region 102, this compression causes the fusion fuel to ignite and thus burn a significant fraction of the fusion fuel in the fuel region 102. Initially the ion and electron temperatures will stay in equilibrium. However, once the burning of the fusion fuel reaches a certain point, the ion temperature will separate from the electron temperature. The point at which the ion temperature greatly exceeds the electron temperature is generally when the fuel enters runaway burn and energy is added to the fuel solely from fusion reactions and not PdV work being done by the shell.

Depending on the type of material (high-Z, medium-Z, low-Z or combinations thereof) present in the fusion fuel in fuel region 102, the fuel region 102 may or may not enter runaway burn. If enough high-Z material is present in the fusion fuel as the fuel reaches ignition conditions, the DT will not enter runaway burn. However, for certain high-Z, medium-Z, or low-Z mixtures in the fuel region 102, the ignition within the ICF target can be controlled. There are various advantages for using some high-Z, medium-Z, or low-Z materials and/or mixtures in the fuel region 102. One benefit is that the radiation coupling properties within a medium-Z material, such as but not limited to Iron, may be more focused and maximize the energy output when igniting an ICF target. It may be advantageous to choose a material which is completely ionized near the ignition temperature of the fuel.

In ICF targets that ignite a DT fuel section having an areal density (ρr) of less than approximately 1 g/cm² (ρr<1 g/cm²) at ignition, the fuel section tends to have a very non-uniform temperature profile. The temperature profile of the fuel section is seen in FIG. 3 , where the mass fraction of DT gas is plotted as a function of temperature. Each of the lines depicted in FIG. 3 represent a different sized target wherein a larger ICF target is represented by the line on the left-hand side with progressively smaller ICF targets to the right. As the areal density (ρr) decreases, the temperature profile becomes less uniform. For an ICF target having a ρr=2 g/cm², all of the DT gas has a temperature below 2.7 keV, however for an ICF target having a smaller areal density such as ρr=0.4 g/cm², the temperature profile becomes less uniform, and some of the DT gas has a temperature above 8 keV. This leads to non-equilibrium ignition where the entirety of the fuel does not ignite at the same point in time. Another attribute of non-equilibrium ignition is a non-uniform density profile. In a non-equilibrium ignition ICF target, there are then many complications which arise in predicting the behavior of the target near ignition since non-uniformities in fuel must be coupled to the properties of the high-Z shell surrounding it and vis a versa. By mixing/combining a small amount of a medium-Z material (<1% by mass) uniformly throughout the DT, one can smooth both the temperature and density profiles in the fuel of non-equilibrium ignition targets without preventing runaway burn or affecting margin parameters such as fall-line greatly. This uniformity reduces the complexity in calculating the stability of the fuel/shell interface immensely.

The fall line parameter (γ_(f)) is defined as the radius at which the shell/fuel interface would have been ignoring effects of deceleration divided by the radius of the interface including the effects of deceleration at the time of stagnation of the shell/fuel interface (see FIG. 4 ).

$\gamma_{f} = \frac{r_{f}}{r_{s}}$

wherein r_(f)=fall-line radius at stagnation and r_(s)=stagnation radius. The ignition time is defined as a time when mass-averaged fuel temperature is 2.5 keV. The shell convergence (C) is defined as the initial inner shell radius over the inner shell radius at stagnation

C=r _(i) /r _(s)

FIG. 5 and Table 1 below, show four scenarios of doping quantities. Each scenario utilizes the same sized ICF target but with varying degrees of a medium-Z material, such as Iron, mixed throughout the mixture of DT gas (0%, 0.1%, 0.25% and 1.0% by mass of iron) in the fuel region 102/202. Iron was simply one of a plurality of possible materials selected and described herein. It would be possible to select medium-Z materials other than Iron or even high-Z materials such as Tungsten, Gold, Uranium-238, etc. Any of these alternative selections would subsequently yield different results than the parameters described herein. As stated above, the phase of the mixture of the plurality of fusion fuel materials transforms when the shock is launched into the fusion fuel region. This phase transformation allows for these materials to be uniformly mixed by any one of a variety of known methods, such as a wet chemical, vapor phase compression, electrochemical, plasma methods, etc. In order to uniformly disperse a medium-Z material like Iron with DT, one must sufficiently stimulate the solution in some way, such that the dispersed fine particles (each containing several molecular or atomic units) begin to collect. By creating physical and chemical interactions between suspended particles and those dispersed in the solution, units of tens of thousands of molecules line up together to form an infinitely large three-dimensional molecule that occupies the entire volume. These known methods offer a flexible approach and allows materials of differing chemistries to be uniformly mixed.

As seen in FIG. 5 and Table 1 below, it is clearly evident that the temperature uniformity increases with increasing iron content. However, as the iron content is increased, other effects can be seen. Iron requires more energy than DT to ionize. If the same amount of energy is present in the fuel region, then the greater the iron content, the later in time the target will ignite, as the iron soaks up energy that would have heated the DT. If the target ignites later in time, the high-Z shell has more time to decelerate. As the high-Z shell decelerates, then the material of the high-Z shell will mix with the fusion fuel mixture (i.e., DT fuel) of the fuel region. This increases the growth of Raleigh-Taylor instabilities on the inside of the shell, causing high-Z material to mix with the DT fuel. If the mix is too severe, the target will fail to ignite. This is also the case for simply increasing the mass of the medium-Z material. For example, as seen in FIG. 6 , at a certain point, increasing the iron content in the fuel will begin to decrease the yield of the target. If too much iron is mixed into the fuel, the target will fail to ignite. Again, this will vary slightly by target design. There is therefore, an optimum for a given target design, both for the Z of the mixed material and its content in relation to the DT.

TABLE 1 Parameters due to Varying Degrees of Iron mixed into the DT (by Mass) 0.0% Fe 0.1% Fe 0.25% Fe 1.0% Fe Convergence 8.79 8.9 10.4 11.2 Fall-line 0.03 0.06 0.08 −0.39 Yield (MJ) 0.97 1.06 1.04 0.81 pr (g/cm²) 0.33 0.34 0.44 0.59

Additionally, the set of embodiments discussed in this application is intended to be exemplary only, and not an exhaustive list of all possible variants of the invention. Certain features discussed as part of separate embodiments may be combined into a single embodiment. Additionally, embodiments may make use of various features known in the art but not specified explicitly in this application.

Embodiments can be scaled-up and scaled-down in size, and relative proportions of components within embodiments can be changed as well. The range of values of any parameter (e.g., size, thickness, density, mass, etc.) of any component of an embodiment of this invention, or of entire embodiments, spanned by the exemplary embodiments in this application should not be construed as a limit on the maximum or minimum value of that parameter for other embodiments, unless specifically described as such. 

1. A method for increasing the stability of an Inertial Confinement Fusion (ICF) system when igniting an ICF target, the method comprising: configuring an ICF target to achieve a uniform temperature and density profile when imploding, the ICF target comprising: a central region, wherein said central region comprises a mixture of a plurality of fusion fuel materials and having an areal density of less than approximately 1 g/cm² at ignition; and a first shell directly surrounding and in direct contact with said central region, wherein said first shell comprises a material having a Z of 48 or greater; doping the mixture of the central region with less than approximately 1% of total mass with a material having a Z between 6 and 47 inclusive, mixed throughout the central region; and increasing the stability of a interface between the central region and first shell by adjusting the doping quantity.
 2. The method of claim 1, configuring the mixture of the central region to further comprise: a material having a Z of 48 or greater in addition to the material having a Z between 6 and 47 inclusive, mixed throughout the central region.
 3. The method of claim 2, further comprising: configuring the mixture of the central region to have an areal density of less than approximately 0.5 g/cm² at ignition.
 4. The method of claim 3, further comprising: doping the mixture of the central region with less than approximately 0.5% of total mass with a material having a Z between 6 and 47 inclusive, mixed throughout the central region.
 5. The method of claim 4, further comprising: doping the mixture of the central region with less than approximately 0.25% of total mass with a material having a Z between 6 and 47 inclusive, mixed throughout the central region.
 6. The method of claim 5, wherein the material having a Z between 6 and 47 inclusive, is Iron.
 7. The method of claim 6, further comprises: configuring the ICF target to include an outer fuel region and outer shell, wherein said outer shell directly surrounds said outer fuel region which directly surrounds said first shell which directly surrounds said inner fuel region.
 8. The method of claim 7, further comprising: uniformly mixing the plurality of fusion fuel material throughout the central region.
 9. The method of claim 1, further comprising: configuring the mixture of the central region to have an areal density of less than 0.7 g/cm².
 10. The method of claim 9, further comprises: configuring the ICF target to include an outer fuel region and outer shell, wherein said outer shell directly surrounds said outer fuel region which directly surrounds said first shell which directly surrounds said inner fuel region.
 11. A system for increasing the stability of an Inertial Confinement Fusion (ICF) system when igniting an ICF target, the system comprising: an ICF target to achieve a uniform temperature and density profile when imploding, the ICF target comprising: a central region, wherein said central region comprises a mixture of a plurality of fusion fuel materials; a first shell directly surrounding and in direct contact with said central region, wherein said first shell comprises a material having a Z of 48 or greater; wherein the mixture of the central region has an areal density of less than approximately 1 g/cm² at ignition; wherein at least one of the plurality of fusion fuel materials from the mixture in the central region has less than approximately 1% of total mass of a material having a Z between 6 and 47 inclusive, mixed throughout the central region.
 12. The system of claim 11, the central region further comprising: the mixture to include a material having a Z of 48 or greater in addition to the material having a Z between 6 and 47 inclusive, uniformly mixed throughout the central region.
 13. The system of claim 12, further comprising: the mixture of the central region to have an areal density of less than approximately 0.5 g/cm² at ignition.
 14. The system of claim 13, further comprising: at least one of the plurality of fusion fuel materials from the mixture in the central region to have less than approximately 0.5% of total mass, a material having a Z between 6 and 47 inclusive mixed throughout the central region.
 15. The system of claim 14, further comprising: at least one of the plurality of fusion fuel materials from the mixture in the central region to have less than approximately 0.25% of total mass, a material having a Z between 6 and 47 inclusive mixed throughout the central region.
 16. The system of claim 15, wherein the material having a Z between 6 and 47 inclusive, is Iron.
 17. The system of claim 16, wherein the ICF target further comprises: an outer fuel region and outer shell, wherein said outer shell directly surrounds said outer fuel region which directly surrounds said first shell which directly surrounds said inner fuel region.
 18. The system of claim 17, further comprising: the plurality of fusion fuel material are uniformly mixed throughout the central region.
 19. The system of claim 11, wherein the ICF target further comprises: the central region having an areal density of less than 0.7 g/cm².
 20. The system of claim 19, wherein the ICF target further comprises: an outer fuel region and outer shell, wherein said outer shell directly surrounds said outer fuel region which directly surrounds said first shell which directly surrounds said inner fuel region. 